A-Level Further Maths · Year 13 · Further Mechanics
Further Centres of Mass worksheets with answers
Free worksheets for the 7 lessons in A-Level Further Maths Further Centres of Mass, written by qualified teachers. Each lesson has a worksheet, full answers to the worksheet and a homework sheet, as PDFs to print or share. No sign-up needed.
7 lessonsAQA 7367 · Edexcel 9FM0
We don't publish answers to the homework, so teachers can set it as independent work.
Lesson 1 of 7
Laminas by Integration
Finds the centre of mass of a uniform lamina under a curve, or between two curves, by splitting it into thin strips and integrating. Students also prove a standard result, find the centre of mass of a non-uniform rod, and find unknown constants and the angle at which a lamina hangs.
- AQA 7367
- ME3 (lamina by integration)
- Edexcel 9FM0
- FM2 Further centres of mass (laminas and non-uniform rods by integration)
Lesson 2 of 7
Solids of Revolution by Integration
Finds the centre of mass of solids of revolution by splitting them into thin discs and integrating, including proofs of the standard results for a cone and a hemisphere. Students apply this to paraboloids, frustums and composite solids, and find the angle at which a solid hangs.
- AQA 7367
- ME4 (solids of revolution by integration)
- Edexcel 9FM0
- FM2 Further centres of mass (uniform and non-uniform solids of revolution)
Lesson 3 of 7
Sliding or Toppling under an Applied Force
Decides whether a body on rough ground, pushed or pulled by a force, slides or topples first, by resolving forces and taking moments about the front edge. Students find the range of the coefficient of friction, of the height of the force, or of the force itself.
- AQA 7367
- ME5 (sliding and toppling)
- Edexcel 9FM0
- FM2 Further centres of mass (sliding and toppling)
Lesson 4 of 7
Sliding or Toppling on an Inclined Plane
Decides whether a body on an inclined plane slides or topples first, using the centres of mass found in the earlier units. Students also find the least and greatest force that holds a body on a slope, checking that it does not topple.
- AQA 7367
- ME5 (sliding and toppling)
- Edexcel 9FM0
- FM2 Further centres of mass (toppling of a lamina on an inclined plane; solids A level only)
Lesson 5 of 7
Moments and Couples
Finds the moment of a force about a point and the moment of a couple. Students reduce a system of forces in a plane to a single force, a couple, or a force and a couple, and use equilibrium to find unknown forces. This content is on the AQA specification only.
- AQA 7367
- ME6 (moments and couples; A level only)
- Edexcel 9FM0 FM2
- not examined
Lesson 6 of 7
Rigid Bodies in Equilibrium
Solves equilibrium problems for rigid bodies such as ladders and rods resting on pegs or in bowls, by resolving in two directions and taking moments about one point. Students use friction at rough contacts and the geometry of smooth contacts. This content is on the AQA specification only.
- AQA 7367
- ME6 (rigid bodies in equilibrium; A level only)
- Edexcel 9FM0 FM2
- not examined
Mixed review · Lesson 7 of 7
Unit review: Further Centres of Mass
Mixed exam-style practice across the whole Further Centres of Mass unit: centres of mass by integration, sliding and toppling, moments and couples, and rigid bodies in equilibrium. The moments and rigid-body questions are AQA content only.
- AQA 7367
- ME3, ME4, ME5, ME6
- Edexcel 9FM0
- FM2 Further centres of mass (ME6 content, moments and rigid bodies, is AQA only)
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